Abstract The kinetics of aggregation of non Brownian magnetizable particles in the presence of a magnetic field is studied both theoretically and by means of computer simulations. A theoretical approach is based on a system of Smoluchowski equations for the distribution function of the number of particles in linear chain-like aggregates. Results obtained in the two dimensional (2D) and three dimensional (3D) models are analyzed in relation with the size of the cell, containing the particles, and the particle volume fraction φ. The theoretical model reproduces the change of the aggregation kinetics with the size of the cell and with the particle volume fraction as long as the lateral aggregation of chains is negligible. The simulations show that lateral aggregation takes place when, roughly, φ2D>5% and φ3D>1.5%. Dependence of the average size of the chains with time can be described by a power law; the corresponding exponent decreases with the particle volume fraction in relation with the lateral aggregation. In the 3D simulations, dense labyrinthine-like structures, aligned along the applied field, are observed when the particle concentration is high enough (φ3D>5%).